A conformally indecomposable flow f on a signed graph Σ is a nonzero integral flow that cannot be decomposed into f = f1 + f2, where f1, f2 are nonzero integral flows having the same sign (both ≥ 0 or both ≤ 0) at every edge. This paper is to classify at integer scale conformally indecomposable flows into characteristic vectors of Eulerian cycle-trees — a class of signed graphs having a kind of...

A class of indecomposable representations of Uq(s`n) is considered for q an even root of unity (qh = −1 ) exhibiting a similar structure as (height h ) indecomposable lowest weight Kac-Moody modules associated with a chiral conformal field theory. In particular, Uq(s`n) counterparts of the Bernard-Felder BRS operators are constructed for n = 2, 3 . For n = 2 a pair of dual d2(h) = h dimensional...

We study some relations between a reproducing cone K in a linear space V over a fully ordered field F and the cone I(K) in Hom( V, V) consisting of all operators A such that AK G K. In particular, indecomposable cones are considered.

It is well-known that each nonnegative integral flow of a directed graph can be decomposed into a sum of nonnegative graph circuit flows, which cannot be further decomposed into nonnegative integral sub-flows. This is equivalent to saying that indecomposable flows of graphs are those graph circuit flows. Turning from graphs to signed graphs, the indecomposable flows are much richer than that of...

We consider the continuum scaling limit of the infinite series of Yang-Baxter integrable logarithmic minimal models LM(p, p′) as ‘rational’ logarithmic conformal field theories with extendedW symmetry. The representation content is found to consist of 6pp′ − 2p− 2p′ W-indecomposable representations of which 2p+2p′ − 2 are of rank 1, 4pp′ − 2p− 2p′ are of rank 2, while the remaining 2(p− 1)(p′ −...

Cyclically Indecomposable Triple Systems that are Decomposable Martin Grüttmüller Institut für Mathematik, Universität Rostock In this talk, we construct, by using Skolem-type and Rosa-type sequences, cyclically indecomposable two-fold triple systems TS2(v) for all admissible orders. We also investigate exhaustively the cyclically indecomposable triple systems TSλ(v) for λ = 2, v ≤ 33 and λ = 3...

Let p be an odd prime. In this paper we study the relationship between degeneracy and decomposability in abelian crossed products. In particular we construct an indecomposable abelian crossed product division algebra of exponent p and index p. The algebra we construct is generic in the sense of [AS78] and has the property that its underlying abelian crossed product is a decomposable division al...

Beimel, Tassa and Weinreb (2008) and Farras and Padro (2010) partially characterized weighted simple games that are access structures of ideal secret sharing schemes; they did this in terms of the operation of composition of simple games. They classified such indecomposable weighted games, and proved that any other weighted game, which is the access structure of an ideal secret sharing scheme, ...